Question

Question:Consider the following statements. Write out an example reaction and K expression that are associated with each statement.

a. The autoionization of water.

b. An acid reacts with water to produce the conjugate base of the acid and the hydronium ion.

c. A base reacts with water to produce the conjugate acid of the base and the hydroxide ion.

Short answer

Answer

The equilibrium constant is the ratio of product and reactant concentrations. It is calculated using an ionic equation.

For autoionization of water,

$2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-}:\mathrm{K}=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]$

An acid reacts with water to produce the conjugate base of the acid and the hydronium ion:

$$\begin{gathered} {\mathrm{HA}}_{\left(\mathrm{aq}\right)}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{A}}^{-}+{\mathrm{H}}_3{{\mathrm{O}}^{+}}_{\left(\mathrm{aq}\right)} \\ {\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{A}}^{-}\right]\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]}{\left[\mathrm{HA}\right]} \end{gathered}$$

A base reacts with water to produce the conjugate acid of the base and the hydroxide ion:

$$\begin{gathered} {\mathrm{B}}^{-}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{BH}}_{\left(\mathrm{aq}\right)}+{{\mathrm{OH}}^{-}}_{\left(\mathrm{aq}\right)} \\ {\mathrm{K}}_{\mathrm{b}}=\frac{\left[\mathrm{BH}\right]\left[{\mathrm{OH}}^{-}\right]}{{\mathrm{B}}^{-}} \end{gathered}$$

Step-by-step solution

Equilibrium Constant Expression

Equilibrium constant represents the ratio of the product of the equilibrium concentrations of the products, which are raised to their coefficients in the balanced chemical equation, to the product of the equilibrium concentrations of the reactants.

$$\begin{gathered} \mathrm{For}\mathrm{the}\mathrm{reaction},\mathrm{aA}\rightleftharpoons \mathrm{cC} \\ \mathrm{K}=\frac{{\left[\mathrm{C}\right]}^{\mathrm{c}}}{{\left[\mathrm{A}\right]}^{\mathrm{a}}} \end{gathered}$$

The Autoionization of Water and its k Expression 

$$\begin{gathered} \mathrm{Autoionization}\mathrm{of}\mathrm{water},2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-} \\ \mathrm{K}=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{OH}}^{-}\right] \end{gathered}$$

The Reaction of an Acid with Water and its equilibrium constant expression

The reaction can be represented as:

$$\begin{gathered} {\mathrm{HA}}_{\left(\mathrm{aq}\right)}+{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{aq}\right)}\rightleftharpoons {{\mathrm{A}}^{-}}_{\left(\mathrm{aq}\right)}+{\mathrm{H}}_3{{\mathrm{O}}^{+}}_{\left(\mathrm{aq}\right)} \\ {\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{A}}^{-}\right]\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]}{\left[\mathrm{HA}\right]} \end{gathered}$$

The Reaction of a Base with Water and its Equilibrium constant expression

The reaction can be represented as:

$$\begin{gathered} {{\mathrm{B}}^{-}}_{\left(\mathrm{aq}\right)}+{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)}\rightleftharpoons {\mathrm{BH}}_{\left(\mathrm{aq}\right)}+{{\mathrm{OH}}^{-}}_{\left(\mathrm{aq}\right)} \\ {\mathrm{K}}_{\mathrm{b}}=\frac{\left[\mathrm{BH}\right]\left[{\mathrm{OH}}^{-}\right]}{\left[{\mathrm{B}}^{-}\right]} \end{gathered}$$